已知数列{an}满足a1=1,an+1=2an/(an+2)(n∈N+),则数列{an}的通项公式为
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已知数列{an}满足a1=1,an+1=2an/(an+2)(n∈N+),则数列{an}的通项公式为
已知数列{an}满足a1=1,an+1=2an/(an+2)(n∈N+),则数列{an}的通项公式为
已知数列{an}满足a1=1,an+1=2an/(an+2)(n∈N+),则数列{an}的通项公式为
a(n+1)=2an/(an+2)
1/a(n+1)=(an+2)/(2an)=1/an+1/2
1/a(n+1)-1/an=1/2,为定值.
1/a1=1/1=1
数列{1/an}是以1为首项,1/2为公差的等差数列.
1/an=1/a1+(n-1)(1/2)=1+(n-1)/2=(n+1)/2
an=2/(n+1)
n=1时,a1=2/(1+1)=1,同样满足.
数列{an}的通项公式为an=2/(n+1).
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